I finally get REST. Wow.
The essence of REST is to make the states of the protocol explicit and addressible by URIs. The current state of the protocol state machine is represented by the URI you just operated on and the state representation you retrieved. You change state by operating on the URI of the state you're moving to, making that your new state. A state's representation includes the links (arcs in the graph) to the other states that you can move to from the current state.